mine was very nervous of dark rides to start with - now she is quite happy on Pirates, but will not even consider the Haunted Mansion - i can't imagine her ever going on it, she is that concerned about it. She also hates the Snow White ride not that she has ever ridden it, but she's seen it on the video and she knows the witch is in there.
I would suggest starting with It's a Small World - it's not particularly dark - Nothing remotely scary happens, but it gives them a good idea of how the rides work and what is likely to happen - nothing like a good positive experience to start off the day. Pooh is pretty good too, although the Heffalump scene worried my dd a little bit, but she was basically ok with it.
Also, we bought a light-up Pooh Bear wand in the park, and we carried this with us, pooh didn't work well outside as it was too bright, so it became a bit of a treat to go inside someplace dark enough for Pooh to work -
Bev